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A ball is dropped from a height of 10 m. If the energy of the ball reduces by 40 % after striking the ground, how high can the ball bounce back? (g = $10m{{s}^{-2}}$)
(A) 6 m
(B) 10 m
(C) 3 m
(D) 1 m

Last updated date: 13th Jun 2024
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Hint: We know that in physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. On the other hand, potential energy is energy that is stored or conserved in an object or substance. This stored energy is based on the position, arrangement or state of the object or substance. We can think of it as energy that has the 'potential' to do work. Based on this concept we have to solve this question.

Complete step by step answer
We know that the total energy of the ball is given as$=\mathrm{m} \mathrm{g} \mathrm{h}$
After we put the value of the height we get as $=\operatorname{mg} 10$
We can also write this as:
$=100 \mathrm{m} \mathrm{kgm}^{2} \mathrm{s}^{-2}$
It is known that energy with which it moves up the ground after striking = $60 \%$ of the total energy $\mathrm{E}=\dfrac{60}{100} \times 100 \mathrm{m} \mathrm{kgm}^{2} \mathrm{s}^{-2}$
Height to which the ball will bounce back $\mathrm{h}=\dfrac{\mathrm{E}}{\mathrm{m} \times \mathrm{g}}=6$ meter
So, the height at which the ball will bounce back is 6 m.

Hence, the correct answer is option A.

Note: We should know that kinetic energy is built up in an object by motion and can be defined as the energy that is needed to either slow it down or speed it up. Studies have also been done using kinetic energy and then converting it to other types of energy, which is then used to power everything from flashlights to radios and more. Energy is transferred from one object to another when a reaction takes place. Energy comes in many forms and can be transferred from one object to another as heat, light, or motion, to name a few.
On the other hand, potential energy becomes useful when it is converted to kinetic energy. Kinetic energy is used to perform work. Work occurs when force is applied to an object. Kinetic energy is useful because it allows work to be done. Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as a spring or the force of gravity. This work is stored in the force field, which is said to be stored as potential energy.